STANFORD CENTER FOR INTERNATIONAL DEVELOPMENT

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1 STANFORD CENTER FOR INTERNATIONAL DEVELOPMENT Working Paper No. 214 Organized Crime, Corruption, and Punihment by Maurice Kugler *, Thierry Verdier ** and Yve Zenou *** May 2004 Stanford Univerity 579 Serra alvez, Landau Economic Building, Room 153 Stanford, CA * Univerity of Southampton ** DELTA-ENS *** Univerity of Southampton and AINS

2 Organized Crime, Corruption and Punihment Maurice Kugler Thierry Verdier Yve Zenou May 2004 Abtract We analyze an oligopoly model in which differentiated criminal organization globally compete on criminal activitie and engage in local corruption to avoid punihment. When law enforcer are ufficiently well-paid, difficult to bribe and corruption detection highly probable, we how that increaing policing or anction effectively deter crime. However, when bribing cot are low, that i badly-paid and dihonet law enforcer work in a weak governance environment, and the rent from criminal activity relative to legal activity are ufficiently high, we find that increaing policing and anction can generate higher crime rate. In particular, the relationhip between the traditional intrument of deterrence, namely intenification of policing and anction, and the crime rate i nonmonotonic. Beyond a threhold, further increae in intended expected punihment create incentive for organized crime extending corruption ring, and enuing impunity reult in a fall of actual expected punihment that yield more rather than le crime. JEL Claification: K42, L13, O17. Keyword: Intended deterrence, organized crime, corruption We would like to thank Pranab Bardhan, Edward Chritie, Nick Hope, Larry Lau, David McKenzie, Mitchell Polinky, Eteban Roi-Hanberg, the editor Sören Blomquit, two anonymou referee, a well a eminar participant at the CEPR Public Policy Sympoium in La Coruña, Stanford Univerity and UC Berkeley, for very helpful comment. Kugler acknowledge hopitality from the Stanford Center for International Development. Zenou thank the Marianne and Marcu Wallenberg Foundation for financial upport. Univerity of Southampton. mdk1@oton.ac.uk DELTA-ENS. verdier@delta.en.fr IUI, Univerity of Southampton and AINS. yvez@iui.e 1

3 1 Introduction There are occaional example of ucceful battle againt the corruption perpetrated by criminal organization to influence law enforcement and politic. For example, in 1931, right after prohibition of alcohol conumption ended in the United State, the conviction of the notoriou gang leader Al Capone for tax evaion led to the break up of mob and racket built around the ditribution of alcohol, and other complementary activitie. Yet, failed attempt to curb the influence of organized crime are common place. Recently, in Italy, the invetigation mani pulite (clean hand) initiated by a courageou group of judge diintegrated after dicloing pervaive corruption by the Mafia. Thi effort wa halted by a tring of aaination inflicted upon law enforcer and their familie. In general, organized crime yndicate are very difficult to eliminate. They are able to protect themelve by a combination of mean: (i) corruption of law-enforcement official; (ii) phyical violence againt informant and witnee; (iii) violent threat againt proecutor, judge and member of jurie; (iv) ue of lawyer to manipulate the legal ytem; and (v) financial contribution to political campaign. The objective of thi paper i to better undertand the complex relationhip between organized crime, corruption and the efficiency of the jutice ytem. We will in fact focu on the evaion from conviction by criminal organization through bribing law enforcer. However, the relevance of our finding i not confined to the influence on the operation of the legal ytem exerted through thi channel. A long a organized crime can invet to manipulate the incentive faced by the actor involved in making proecution poible, our reult regarding the limited effectivene of typical crime deterrent in weak governance environment hold. Criminal gang are active and trategic in their effort to bribe policemen. Cooperative police officer are helpful to criminal gang by paing information to them about police invetigation and planned raid, and by making deliberate mitake in proecution. Such technical error then enure that the charge againt the criminal will not reult in guilty verdict. Corruption of police officer i made eaier by the fact that they are modetly paid and, therefore, are ubject to temptation. Moreover, like proecutor and member of jurie, law enforcer can be coerced through violence. Alo, once a few po- 2

4 licemen have been corrupted, they will make trong effort to enure that their colleague are alo corrupted. An honet policeman who trie to inform on hi corrupt colleague will come under the mot evere preure from them. The economic literature on crime ha emphaized the deterrence capacity of the jutice ytem (e.g. Becker 1968, Ehrlich, 1973, Levitt, 1998). Recent evidence for the United State tend to upport the hypothei that the expectation of potential criminal with repect to punihment determine crime rate (ee e.g. Levitt, 1997). Yet, expected punihment depend not only on the everity of entence but alo on the probability of conviction once crime i perpetrated. The latter depend on detection by the police, proecution by attorney and the deliberation of judge and jurie. A long a thee three activitie are conducted tranparently and efficiently, tough anction will deliver deterrence of criminal activity. 1 However if, a decribed above, corruption i pervaive, then the deterrence capacity of rie in intended expected punihment can be very much reduced due to flawed law enforcement. Since Becker and Stigler (1974) firt acknowledged that malfeaance by enforcer can diminihthe effectivene of law and anction in controlling crime, the literature on crime ha conidered the problem of bribed official. Becker and Stigler propoe the payment of efficiency wage to prevent bribe taking. 2 Beley and McLaren (1993) and Mookherjee and Png (1995) alo propoe wage regime to mitigate the moral hazard problem when rent eeker attempt to co-opt law enforcer. Like Becker and Stigler (1974), Bowle and aroupa (1997) conider a model in which bribery reduce punihment and thu deterrence. However, their focu i different ince it i on the effect of bribery on the optimal allocation of reource (which incorporate the ocial cot of both crime and corruption) within the public enforcement agency. They how that the maximal fine may not be optimal. Chang et al. (2000) extend Bowle and aroupa (1997) by introducing ocial tigma cot for caught corrupt officer. They how that, when corruption i widepread, ocial norm cannot generate aufficient anction to deter corrupt officer, and raiing fine can in fact reult 1 It i alo well-known that, when expected detection i itelf endogenou and negatively depend on the number of criminal, multiple equilibria in crime and deterrence may emerge (ee for intance Fender, 1999, or Sah, 1991). 2 For a comprehenive urvey on law enforcement, ee Polinky and Shavell (2000). Alo, for a general urvey on corruption and development, ee Bardhan (1997). 3

5 in more crime. Another extenion of Bowle and aroupa (1997) i done by aroupa and Jellal (2002). They conider the role of aymmetric information on the emergence of colluion between criminal and enforcer. They how that aymmetric information about the private cot of enforcer engaging in colluion might eventually deter corruption and bargaining between the two partie. Finally, Bau et al. (1992) argue that when the poibility of colluion between law enforcing agent and criminal i introduced, control of corruption become more difficult than i uggeted by the tandard Beckerian approach. Marjit and Shi (1998) extend thi paper and how that controlling crime become difficult, if not impoible, becaue the probability of detection can be affected by the effort of a corrupt official. Finally, in a recent paper Polinky and Shavell (2001) conider the dilution of deterrence caued by corruption not only due to bribing by criminal but alo extortion of the innocent by crooked enforcer. They propoe reward for corruption report to mitigate the breakdown of deterrence. Our approach contribute to the literature in that we focu on the relationhip between organized crime, 3 corruption of law enforcer and punihment of criminal in the context of imperfect competition. Hence, we find not only a reduction in deterrence effectivene due to corruption a in previou model but actually a potential reveral whereby policie uually identified a crime deterrent can intead become inducement a long a bribery remain unchecked. To be more precie, in the preent paper, we analyze the role of corruption not only in diluting deterrence but alo a a trategic complement to crime and therefore a catalyt to organized crime. For that, we develop a imple oligopoly model in which n criminal organization compete with each other on the level of both criminal activitie and corruption. We firt how that when the cot of bribing judge or the number of criminal organization increae, then both crime and corruption decreae wherea when the profitability of crime increae, then both crime and corruption increae. We then how our main reult. If corruption i cotly, due to law enforcer being well-paid, hard to bribe and eaily detected when accepting ide payment, relative to the profit from crime, then, a predicted by the tandard literature on crime, it i alway effective to reduce crime by intenifying policing or toughening anc- 3 There i a mall theoretical literature on organized crime (without corruption). See in particular Fiorentini and Peltzman (1996), aroupa (2000) and Manour et al. (2000). 4

6 tion. However, in the revere cae of low-paid dihonet law enforcer under weak governance and izable rent from illegal activity relative to the outide lawful option, increaing policing or anction may in ome cae generate higher crime rate. Thi lat reult i fairly intuitive. A long a the return to legal economic activity i ufficiently low relative to rent from crime, gang continue puring crime. When anction and policing are toughened, the cot of hiring criminal rie a there i a wage premium to compenate for the rik of conviction if apprehended. Thi will dicourage crime but only up to a point. In particular, if bribing cot are mall relative to the rent from crime, there i a level of expected punihment beyond which further intended deterrence will induce increaingly higher level of corruption, and of actual crime. Indeed, when governance i weak, harher punihment can be a catalyt for organized crime and may lead to concentration of criminal rent and higher rate of return ex pot. For example, in the 1920 during alcohol prohibition in the United State, mob activitie were o profitable that organized crime could affordtokeepinitpayrollgovernmentofficial at variou level, including elected politician and law enforcer, to influence the legal ytem in it favor. With imperfect competition, the potential effectivene of traditional deterrence policie to top organized crime and other ubidiary illegal activitie i limited. Thi doe not imply that tough anctioning of crime and policing hould be abandoned altogether when intitutional check and balance are underdeveloped. But, rather that unle corruption i curbed, traditional deterrence meaure can have the pervere effect of making crime and corruption trategic complement. After thi introduction, Section 2 et up the model by decribing the problem of the criminal organization. Section 3 characterize the corruption market. In Section 4, the interaction between crime and corruption i analyzed and the main propoition are preented. Section 5 analyze the free-entry equilibrium. Finally, Section 6 conclude the paper by dicuing ome implication of the reult obtained. 5

7 2 The model There are n criminal organization in the economy. Thee organization compete with each other on crime but are local monoponie in the corruption market. On the crime market (think for example of illicit drug cartel), there i a pie to be hared and Cournot competition take place. On the corruption market, there i a continuum of judge to bribe for each of the n criminal organization. A thi will become clear below, crime i global wherea corruption i local. Let u firt decribe the profit function. For each criminal organization, the revenue from criminal activitie depend on the number of crime and the ize of the booty per crime. The cot i given by the wage bill accruing the criminal and the bribe paid to avoid conviction when crime are detected. For the criminal organization i =1,..., n, profit are given by: π(c, C i, α) =B (C) C i w i L i T i (1) where j=n X C = j=1 i the total number of crime perpetrated in the economy, C i denote the number of crime committed by organization i, B (C) i the booty per crime for all criminal organization, with B 0 (C) < 0 (the booty per crime B(C) iaumed to decreae a the number of crime increae), w i, which i determined below, denote the wage paid by each criminal organization i to their L i employed criminal, and T i are the total cot to bribe judge borne by the criminal organization i, alo to be explicitly determined below. For implicity, we aume linear crime profitability and technology, with B(C) =B C and C i = L i. Let u determine the wage w i. Thoe upplying labor are rik neutral. The participation contraint for a given criminal working for organization i i given by: φ [w i (α i.0+(1 α i )S)] + (1 φ)w i w 0 (2) where 0 < φ < 1 i the probability of detection of a crime, α i denote the probability that a judge i corrupted by organization i, S>0itheanction 6 C j

8 when punihment of detected crime i enforced and w 0 > 0 i the outide legal wage for individual not engaged in criminal activitie. In equation (2), the left hand ide give the expected gain of a criminal. Indeed, if he/he i not caught (with probability 1 φ), he/he get w i. If he/he i caught (with probability φ), he/he till obtain w i (we aume that criminal get their wage even when they are caught) but might be convicted and punihed. In particular, if the judge i bribed by organization i (with probability α i ), the criminal i not anctioned wherea if the judge i not bribed by organization i (with probability 1 α i ), the criminal face anction S (thi repreent, for example, the number of year in prion). Thi i a key incentive for a criminal to join organized crime. Apart from getting w i independently of detection, he/he benefit from not being punihed by anction S even if caught when aigned to a judge in the payroll of organization i. In equilibrium, thi contraint i binding ince there i no incentive for the criminal group to pay more than the outide wage. Therefore, the reervation wage for which worker accept to commit crime for organization i i equal to: w i = φs(1 α i )+w 0 (3) Interetingly, in equilibrium, thi wage will be determined by the level of corruption α i in each organization ince the higher the level of corruption, the lower i the rik premium commanded by criminal. Indeed, if the rik of conviction for a criminal i low, then, a long a w i i greater than w 0 (which i alway the cae; ee (3)), there i no need to pay a much higher wage. 3 Corruption The interaction between criminal organization and judge i modeled here by mean of a monoponitic competitive market inpired by Salop (1979). For that, we conider n local market (for example region or local area); each of them i decribed by the circumference of a circle which ha length 1. In each local market, there i one criminal organization and a continuum of judge uniformly ditributed on the circumference of the circle; the denity i contant and equal to 1. Without lo of generality, organization i (= 1,...n) location i normalized to 0. The pace in which each criminal organization and judge are located i interpreted a the tranaction cot pace. A a reult, criminal 7

9 organization compete with each other on crime, i.e. crime i global, wherea they only bribe judge locally, i.e. corruption i local. Thi mean that, if a criminal belonging to organization i i caught, he/he will be proecuted by a judge located in market i. In other word, all criminal commit crime in a common market but criminal belonging to different organization are proecuted in ditinct market. For example, for crime related to narcotic ditribution, drug cartel deal illicit ubtance acro many different geographic market but criminal are proecuted in the juridiction where their cartel operation originate. Contrary to the tandard patial model (Salop, 1979), the horizontal differentiation of judge take place from the point of view of criminal organization. In other word, the latter are paying all the tranaction cot needed to bribe a judge (i.e. delivery cot accrue to the buyer). From the judge point of view, there i no differentiation ince they will accept a bribe if and only if their expected gain i greater than their current wage. A a reult, the ditance ofajudgetoacriminalorganizationreflect the tranaction cot neceary to agree on a bribe. A ocial network formation may be baed on regional, ethnic or religiou affinity, cloene between gang leader and law enforcer along any of thee dimenion facilitate bribing. If we take the geographic example of Italy, it i eaier for a criminal organization originating in Sicily to bribe a judge located in Palermo than in Milan becaue it ha more contact with local who peak the ame dialect. In the model, judge location type are denoted by x. The more ditant, the higher the tranaction cot to bribe a judge. The tranaction cot function between a criminal organization located in 0 and a judge x i t x, wheret expree the tranaction cot per unit of ditance in the location pace. We aume that the outide option for judge i their current wage w b, a corrupt law enforcer caught accepting bribe loe their job. In thi paper, we focu on non-covered corruption market, i.e. market in which ome of the judge do not accept bribe and are thu not corrupted. We believe it i much more realitic than a covered market in which all judge will be corrupted in equilibrium. Thi mean that each criminal organization act a a local monopony on the corruption market wherea they will compete a la Cournot on the crime market. Denote by x i the boundary of the egment correponding to each monoponit i. Thi implie that each criminal organi- 8

10 zation will bribe 2x i judge in equilibrium. Since each criminal organization i alone in it corruption market, we have to check that x i < 1/2, i =1,..., n, o that, in equilibrium, the corruption market i not covered. Oberve that, even if the proecution and thu the corruption are local, the probability to be proecuted by a corrupted judge i never 1. Indeed, when a criminal belonging to organization i i caught, one know that he/he will be judged in local market i butdoenotknowthejudgetowhichthecaeitobeaigned.thii why the probability to be proecuted by a corrupted judge in region i i 2x i, which i by aumption trictly le than 1. All judge are rik neutral. The participation contraint for a judge who i bribed by a criminal organization i located at a ditance x i i thu given by (1 q)(f + w b ) w b where q i the probability that corruption i caught (quite naturally, we aume that if a judge i caught, he/he loe hi/her wage w b )andf i the bribe given to the judge. Oberve that f i not indexed by i ince on the corruption market each criminal organization ha total monopony power and thu fixe a bribe that jut bind the judge participation contraint. The latter only depend on q and w b. Once again, the left hand ide give the expected benefit from corruption wherea the right hand ide decribe the opportunity cot. The anction for corruption i the lo of the job and the bribe. A a reult, for each organization i = 1,...,n the bribe neceary to corrupt a judge i given by f = q 1 q w b (4) A tated above, all judge are identical o that at f they will alway accept a bribe. We could have aumed that the bribe i f + ε, whereε i very mall but poitive; thi would obviouly not change our reult o whenever judge are indifferent they accept to be bribed. However, from the criminal organization point of view each judge i not located at the ame ditance o that the tranaction cot to bribe a judge i different from one judge to another. Since x i i the maximum ditance acceptable for each criminal organization i (i.e. beyond x i the tranaction cot of bribing a judge i too high), then the total tranaction cot for each criminal organization i i given 9

11 by: 4 T i =2 Z xi 0 (f + t)xdx =(f + t)x 2 i In thi context, ince the length of the circumference of the circle i normalized to 1, the probability α i (the fraction of law enforcer that will be bribed in equilibrium by paying to each of them a bribe f) igivenbyα i =2x i /1=2x i. Taking into account all the element (in particular the participation contraint of each criminal (3) and the participation contraint of each judge), and uing (1), the profit function of a criminal organization can be written a: Ã! j=n X π(c, C i,f)= B C j C i [φs (1 2x i )+w 0 ] C i (f + t)x 2 i (5) j=1 Thi profit function of each criminal organization i divided in three part. The firt one i the proceed from crime, which depend on the competition in the crime market between the different crime organization. The econd correpond to the alary cot of hiring criminal while the third part denote the cot of bribing judge. From thi reduced form, the link between crime and corruption can be een. While the marginal cot of bribing i increaing, corruption reduce the unit cot per crime a the wage rik premium paid to criminal fall. 4 Crime and corruption A tated above, criminal organization compete on both crime and corruption. On the crime market, each criminal organization i compete a la Cournot by determining the optimal C i. On the corruption market, each act a local monoponit by determining the optimal x i (indeed, they have to determine 4 If we take a geographical interpretation, then the total cot (f + t)x of bribing a judge located at a ditance x from a criminal organization i a follow. The criminal organization hato travel aditancex, atacott per unit of ditance, to ee the judge and then ha to bribe him/her, at a cot f per unit of ditance, i.e. the cot of bribing a judge depend on the phyical ditance between thi judge and the criminal organization. In fact, we aume that there i a perfect correlation between the phyical ditance and the bribe ditance between a criminal organization and a judge, even though the cot per unit of ditance i different, i.e. t 6= f. 10

12 the maximum ditance x i beyond which it i not profitable corrupting a judge). Becaue, in thi model, judge are baically belong to the payroll of criminal organization, the choice of C i and x i are imultaneou. Thu, chooing imultaneouly C i and x i (oberve that there i a one-to-one relationhip between x i and α i ) that maximize the profit (5) yield the following firt order condition: j=n X B C j C i [φs (1 2x i )+w 0 ]=0 (6) j=1 2φSC i 2(f + t)x i =0 (7) Uing the Heian matrix, it i eay to verify that the profit function (5) i trictly concave (implying a unique maximum) if and only if: f + t>2(φs) 2 (8) Let u now focu on a ymmetric equilibrium in which C i = C j = C and x i = x j = x for all i 6= j with 1 i n and 1 j n. The firt order condition are now given by: B (n +1)C = φs (1 2x )+w 0 (9) Now, from (9) we obtain φsc =(f + t)x (10) C = B w 0 φs (1 2x ) n +1 (11) Plugging (11) into (10) yield x = Then, by plugging (12) into (11), we have We have finally the following reult. φs (B w 0 φs) (f + t)(n +1) 2(φS) 2 (12) C = (f + t)(b w 0 φs) (f + t)(n +1) 2(φS) 2 (13) 11

13 Propoition 1 Aume p(f φs <min + t)/2,b w0, (f + t)(n +1) 2(B w 0 ) (14) Then, there i a unique equilibrium C and α =2x,wherethenumber of crime per criminal organization C i given by (13) and the meaure of corrupted judge per criminal organization α =2x by (12). Both of them are trictly poitive and (1 α ) n judge are not corrupted in equilibrium. Moreover,theequilibriumprofit of each criminal organization i given by π (n) = (f + t)(b w 0 φs) 2 (f + t (φs) 2 ) [(f + t)(n +1) 2(φS) 2 ] 2 > 0 (15) and the wage paid to each criminal i equal to w (n) =φs (f + t)(n +1) 2φS (B w 0) (f + t)(n +1) 2(φS) 2 + w 0 >w 0 (16) Proof. See the Appendix. The following comment are in order. Firt, condition (14) guarantee that both C and x are trictly poitive and that the olution of the maximization problem i unique. Condition (14) alo enure that, in equilibrium, ome judge are not corrupted (i.e. x < 1/2). Indeed, the difference between the booty B and the wage of an individual having a regular job (i.e. working in the legal ector) ha to be large enough to induce criminal organization to hire criminal and to bribe judge. At the ame time, thi difference ha to be bounded above otherwie all judge will be corrupted becaue the profitability per crime would be o large to yield a corner olution in bribing. Second, when chooing C the optimal number of criminal to hire, each criminal organization face two oppoite effect. When it increae C, the proceed from crime are higher (poitive loot effect) but the competition will be fiercer (negative competition effect) and the wage bill higher (negative alary effect). A a reult, chooing the optimal C reult from a trade-off between the firt poitive effect and the econd and third negative effect. Thi trade-off i reflected inthefirt order condition (9). Finally, when chooing x the level of corruption, each criminal organization only face two effect (there i no competition ince each criminal organization act a a monoponit in it corruption market). Indeed, when it increae x, lower payment to criminal increae profit by aving in 12

14 wage (poitive alary effect) ince criminal have le rik to be entenced but the cot of bribing judge rie (negative bribe effect). Thi trade-off i reflected in the firt order condition (10). At thi tage, it i important to quetion the timing of the model in which the choice of C i and x i are imultaneou, implying that ome judge are baically permanent employee of criminal organization. Another poibility would have been that criminal organization commit crime firt, and then, when detected, invet reource to bribe the judge to which the cae ha been aigned. In that cae, the timing would have been that C i i choen firt and then x i i decided. It i eay to verify that uing thi timing, we would have obtained exactly the ame reult a uing the imultaneou choice timing, i.e. C and x will till be given by (13) and (12). Thi i becaue in both cae crime doe not have trategic effect on corruption, i.e. C i (crime committed by all other competing organization but i) hanoeffect on x i (ee equation (7)). However, if the timing wa to chooe firt x i and then C i,itieayto verify that C i would depend both on x i and x i, and, in thi cae, the reult would dratically change. But, with thi timing, the economic interpretation doe not make very much ene ince it implie that criminal organization would decide on corruption before even committing crime. It i now intereting to analyze the propertie of the equilibrium. We have a firt imple reult. Propoition 2 Aume (14). Then, (i) When f the cot of bribing judge, t the unit tranaction cot of bribing judge or n the number of criminal organization increae, then both crime and corruption decreae. (ii) When the maximum net proceed per crime B w 0 increae, then both crime and corruption increae. Proof. Straightforward from calculation. Not urpriingly, both increaing the direct and tranaction cot of bribing judge (f and t) lead to le crime and to le corruption. Moreover, raiing the number of criminal organization n alo decreaecrimeandcorruptionbecaue competition in the crime market become fiercer and lower profitability feed back to the corruption market. In particular, the incentive to bribe fall with 13

15 competition and when the profitability per crime increae independently of n, then obviouly crime and corruption increae. Let u go further in the analyi. Define (φs) CSX 1 (f + t)(n +1) p (f + t)(n +1) p (f + t)(n +1) 2(B w 0 ) 2 2(B w 0 ) and (φs) CSC 1 B w 0 p (B w 0 ) 2 (f + t)(n +1)/2 The following propoition give our main reult. 5 Propoition 3 Aume (14). Then, (i) If (B w 0 ) 2 2(f + t)(n +1) 2 /(n +2) 2, increaing anction alway reduce crime. However, for mall value of φs, increaing anction increae corruption. But for value of φs larger than (φs) CSX 1,increaing anction decreae corruption. (ii) If 2(f + t)(n +1) 2 /(n +2) 2 < (B w 0 ) 2 (f + t)(n +2) 2 /8, increaing anction monotonically reduce crime and increae corruption. (iii) If (B w 0 ) 2 > (f +t)(n+2) 2 /8, increaing anction alway increae corruption. However, for mall value of φs, increaing anction reduce crime. But for value of φs larger than (φs) CSC 1, increaing anction increae crime. Thi implie that, above a threhold value of φs, riing anction increae both crime and corruption. Proof. See Kugler, Verdier and Zenou (2003). Uing Figure 1a, 1b and 1c that illutrate Propoition 3, we can give the intuition of the main reult. When (B w 0 ) 2 2(f + t)(n +1) 2 /(n +2) 2, in relative term, we have that the labor productivity w 0 i high, the proceed per crime B are low, the probability for a corrupted judge of getting caught q a well a hi/her wage w b are high (ee (4)), and the tranaction cot per ditance unit t to bribe judge are large. From Figure 1a, in thi cae, 5 The technical counterpart of Propoition 3 i Propoition 7, which i given in the Appendix. 14

16 increaing φ the probability that a criminal i caught (e.g. enhancing frequency of crime detection by policemen in the region) and S the anction (e.g. tougher punihment upon conviction) alway reduce crime. Yet, corruption can in fact increae for low value of φs and decreae for high value of φs. The intuition run a follow. When B w 0 i quite low compared to f and t, productivity in the legal ector i high, implying the need of high payoff to compenate criminal, and the revenue per crime are low compared to the high cot of bribing judge. Moreover, it i eay to ee that the negative competition effect and the poitive loot effect are not affected by a variation of φs wherea the negative alary effect i affected ince it becomeevenmorecotlytohirecriminal,atheyhaveahigherrikofbeing caught. So, when φs increae, each criminal organization find it optimal to reduce crime, or more exactly the number of criminal hired, becaue the cot of hiring criminal relatively rie. In the corruption market, when φs increae, the poitive alary effect yield incentive to intenify corruption ince it become more cotly to hire criminal wherea the negative bribe effect i not affected ince the cot of bribing law enforcer i independent of φs. Thi can eaily be een in (10) ince the left hand ide correpond to the alary effect (which depend on φs) and the right hand ide to the bribe effect (which doe not depend on φs). In fact, differentiating the left hand ide of (10) with repect to φs yield: C +(φs) C / (φs). The firt effect C i poitive (i.e. for a given level of crime, a φs rie, each criminal organization increae the level of corruption to induce people to become criminal) wherea the econd one (φs) C / (φs) i negative (i.e. a φs rie, there i le crime and thu there i le incentive to bribe o that corruption decreae). A a reult for low value of φs, with profit-maximizing crime C relatively high, if φs increae, the firt effect dominate the econd effect leading to increaed bribing. For high value of φs, with profit-maximizing crime C relatively low, if φs increae, the econd effect dominate the firt one becaue the crime level C i relatively low and it i optimal for criminal organization to bribe le. When 2(f + t)(n +1) 2 /(n +2) 2 < (B w 0 ) 2 (f + t)(n +2) 2 /8, anction affect monotonically both crime and corruption. In thi intermediate cae, the maximum profit per crime alo bounded above but are higher. A n rie the lower bound depend only on the cot of bribing while the upper bound i a term increaing both with bribing cot and the number of competing 15

17 criminal organization. In thi cae, when φs increae, profit-maximizing crime fall while corruption rie. Thi i an example of a ituation in which bribing dilute deterrence but doe not offet it (ee e.g., Polinky and Shavell, 2001). In the previou cae, corruption alo mitigated deterrence but only for relatively mall φ and S. With both ufficiently intene policing and tough anction, bribery ha not diluting effect on deterrence policie. Figure 1b illutrate thi cae. Let u now interpret the cae when (B w 0 ) 2 > (f + t)(n +2) 2 /8. In thi cae, revenue per crime i ufficiently high relative to productivity in the legal ector o that the quared difference exceed the upper bound of the previou cae. In thi cae, when φs increae, it i alway optimal for criminal organization to increae corruption becaue the reulting gain from the reduction of the criminal wage alway i greater than the rie in cot of bribing law enforcer, which i not affected by φs. In contrat, the profitmaximizing level of crime thi i nonmonotonic with repect to φs. Indeed, a tated above, only the alary effect for both crime and corruption are affected by φs. From equation (11), we verify that the ign of C / (φs) depend on (1 2x )+2φS x / (φs). A we aume non-covered corruption market where x < 1/2, the firt term (1 2x ) i alway negative (i.e. for a given level of corruption, when φs increae, it become more cotly to hire criminal). The econd term 2(φS) x / (φs) i poitive and increaing on φs (i.e. when φs increae, there i more bribing and it become le cotly to hire criminal ince their wage rik premium i lower). For low value of φs, thefirt effect dominate the econd one. Thi i becaue at low level of corruption intenifying policing and anction deter crime by increaing it expected cot. However, for high value of φs, the econd effect dominate the firt one ince the level corruption i quite high and thu neither policing nor anctioning deter crime. Profit-maximizing bribing i an increaing function of φs. In fact, beyond a threhold φs, further corruption reduce the criminal wage enough to elicit a rie in profit-maximizing crime. Thi i our main reult. In a juridiction where crime i profitable relative to legal economic opportunitie, judge are badly-paid and eay to corrupt, we find that for crime ubject to intene policing and evere punihment, further increaing the crime detection probability or the everity of the anction reult in more rather than le crime. In particular, when the expected cot of 16

18 crime rie due to increae in the detection probability and tatutory punihment, the optimal repone of criminal organization to counteract deterrence policy i to increae bribing to lower the conviction probability. If law enforcer can be co-opted into the payroll of criminal organization, pervaive bribing induced by intended deterrence policie can be catalyt to a rie in crime. Thi implie that, in juridiction with weak governance, the policy implication of the tandard crime model may not hold and intead, a our model ugget, crime deterrence policy can only be effective enuing a ubtantial cut down in corruption. In thi cae, a rie in φs beyond a threhold can take the model into a region of the parameter pace where crime and corruption are trategic complement, a long a the equilibrium bribe i bounded. It i intereting to compare our reult with that of Malik (1990). In hi model, individual engage in ocially cotly activitie that reduce their probability of being caught and fined. Thi i comparable to corruption in our model. Hi main finding i to how that it i not necearily optimal to et fine for offene ahighapoible. Thihatheameflavor a our reult (iii) in Propoition 3. There are however important difference between the two model. Firt, contrary to u, Malik (1990) adopt a normative perpective. He focue on an enforcement agency that aim at reducing the ocial cot of avoidance activitie by increaing fine. In our analyi, there i no uch an agency. There i intead competition between criminal organization. In our model, we can conduct poitive analye but cannot make tatement about efficiency. Our reult are comparative tatic reult. If one compare two equilibria with different level of anction, then the one with the highet level of anction i not necearily the one with the lowet level of crime and corruption. Second, hi main reult i driven by the fact that individual are heterogeneou ex ante in their earning abilitie. In our model, all agent are identical ex ante and our main reult i driven by the imperfect competition in the crime and corruption market, and the fact that crime and corruption are trategic complement. The mechanim that lead to the reult, and their nature, i thu quite different in the two model. [Inert Figure 1a, 1b and1c here] We can analyze further the potentially counterproductive effect of intended 17

19 deterrence policie by invetigating cae (iii) in Propoition 3. We have the following reult: Propoition 4 Aume (B w 0 ) 2 > (f + t)(n +2) 2 /8 and (14). Then (i) the lower the labor productivity w 0 in the legal ector, (ii) the higher the booty B per crime, (iii) the eaier it i to bribe law enforcer (i.e. the lower the reervation bribe f and aociated tranaction cot t), and/or (iv) the weaker i the competition between criminal organization (i.e. the lower i n), the lower i the threhold of φs above which crime and corruption become trategic complement, i.e. the more likely that an increae in policing or anction lead to an increae in crime. Proof. Straightforward from calculation. Thi propoition complement our previou reult. It help explain why in ome countrie deterrence work, even if diluted by corruption, while in other itcanhavepervereeffect. The propoition etablihe that in juridiction where productivity i quite low in the legal ector, bribing i pervaive, and criminal organization have high market power, then increaing policing and anction i more likely to trigger trategic complementarity among corruption and crime reulting in a pervere effect of deterrence. Thi reult contrat with the literature that ha poited optimal maximal anction. Firt, Polinky and Shavell (1979) how that if fine collection i cotle and monitoring of criminal activity i cotly, the optimal magnitude of fine correpond to the maximum payable by criminal. When thi maximum fall well hort of the booty from crime, nonmonetary anction are required for deterrence. Since it i not only cotly to apprehend criminal but alo to punih them, Shavell (1987) prove that it i optimal for anction to be impoed with low frequency. Hence, in the cae that the court information i imperfect, deterrence require ufficiently large anction. The tandard reult i that under rik neutrality fine hould be maximal. But, if criminal are rik avere, maximal fine are not bet for deterrence. 6 Thepreenceof 6 Polinky and Shavell (2000) preent the tandard cae with rik neutrality (p.50) and then dicu other reaon why maximal fine may not be optimal (pp ). Firt, marginal deterrence may dictate heterogenou fine acro criminal act ocially harmful in different degree. Second, the potential for general enforcement invetment yield economie 18

20 corruption in Polinky and Shavell (2001) alway dictate higher anction to counter the deterrence-diluting effect of corruption. To the extent that there i perfect competition in criminal activitie, rie in expected cot alway act a deterrent. In contrat, in our model with imperfect competition, until bribery can be eradicated, the intenifying policing and punihment beyond a threhold woren the corruption and crime problem. 5 Free entry It i natural to ak what happen to main reult derived o far with the model if we allow for free entry. In our model, thi entail that we invetigate the formation of criminal organization, given that each of them create their own local corruption market. We would thu like characterize the number of criminal organization that will be created in a given country. Each criminal organization that enter the crime and corruption market mut pay a poitive fixed cot. To determine the number of criminal organization n e we have to olve: π (n e ) =0,whereπ (n) i given by (15). We eaily obtain: 7 Propoition 5 If hp i φs <min (f + t)/2,b w0 (17) and B (f + t) w0 φs f + t (φs) 2 < min f + t 2(φS), 1 2 2φS (18) Then, under free entry, the equilibrium number of criminal organization i given by: n e = 1 (f + t) f + t (φs) 2 (B w 0 φs) (f + t) 2(φS) 2 f + t (19) of cope in monitoring inducing apprehenion probabilitie conitent with deterrence for anction magnitude below the maximal level. 7 The upercript e indicate equilibrium variable under free entry. 19

21 The equilibrium number of criminal and corruption are repectively equal to: C e (f + t) = f + t (φs) 2 (20) x e = φs (f + t) f + t (φs) 2 (21) In thi cae, increaing anction alway increae the crime and corruption level per organization, i.e. C e (φs) > 0 and x e (φs) > 0 Proof. See the Appendix. The following comment are in order. Firt, a in the cae with a fixed number of criminal organization, condition (17) guarantee that C e and x e are trictly poitive and unique. Condition (18) guarantee that n e i trictly poitive and that, at the free entry equilibrium, the market i not covered, i.e. ome judge are not corrupted. In order for a free-entry crime market to remain conitent with non-covered corruption market, it ha to be that the free-entry fixed cot i bounded above. The intuition run a follow. When the fixed cot increae, there are le criminal organization in the economy o le competition for crime. Thi implie that crime, corruption and profit per criminal organization increae. A a reult, for the corruption market not to be covered, i.e. x e < 1/2, it ha to be that i ufficiently low to rule out a corner olution with maximal bribing. Similarly, for n e to be poitive, whereby entry take place in equilibrium, it ha to be that i ufficiently low. Thee two condition are expreed in (18). Second, when there i free entry, the number of criminal organization n e, the crime and corruption level per criminal organization, C e and x e, are repectively given by (19), (20) and (21). It i eay to verify that both C e and x e increae with anction φs. Indeed, when anction increae, the competition in the crime market i reduced and thu C e and x e increae. However, thi i doe not necearily increae the total level of crime n e C e and corruption 2n e x e in the economy. We would like now to verify when our previou reult etablihed in Propoition 3 (iii), both higher crime and corruption in the wake of rie in policing and/or anction, i till valid with entry. The following propoition how that it i till true under ome condition on parameter. 20

22 Propoition 6 If and max f + t (φs) 2 φs 3(f + t) 2(φS) 2 < 1 p f + t f + t, < φs < p (f + t) /2 (22) 2 B w 0 B (f + t) w0 φs f + t (φs) 2 < min f + t 2(φS), 1 2 2(φS) (23) then, under free entry, increaing anction increae the total level of both crime and corruption in the economy, i.e. (n e C e ) (φs) > 0 and (2ne x e ) (φs) > 0 Proof. See the Appendix. Thi propoition how that increaing anction can increae both the total level of crime and corruption in the economy if (23) hold, i.e. the fixed cot ha to be bounded above and below. Indeed, a in Propoition 5, the fixed cot ha to be ufficiently low for the market not to be covered and for criminal organization to enter the market. But, a higher fixed cot generate market power for incumbent criminal organization thereby increaing the profit-maximizing level of crime and corruption C e and x e. Hence, with free entry, only for a ufficiently high i it poible that rie policing and anction exacerbate corruption and crime. Indeed, a low fixed cot implie tiff competition and a relatively high n e, and an increae in φs would reduce n e. In thi cae, each criminal organization raie it level of corruption x e and hire more criminal but the global effect can be lower total crime n e C e becaue there are le criminal organization in the economy. If, on the contrary, i not too low, competition in the crime market i limited. Prevailing competition mitigate the rie in crime per organization to offet the fall in the number of organization. Then, the exit effect that reduce aggregate crime in the wake of introducing deterrence policie i dominated by the rie in crime per organization a bribing take off. Inuchcae,intended deterrence policie can become catalyt to increae crime. 21

23 6 Concluion Thi paper ha pelled out the role of corruption and imperfect competition in preventing the jutice ytem to work efficiently. Indeed, in a model where criminal organization compete a la Cournot on the crime market and act a local monoponit on the corruption market, we have howed that when bribing cot are mall relative to crime profitability, beyond a threhold further policing and anction lead to higher rather than lower crime. We agree with Becker (1968), Ehrlich (1973), Polinky and Shavell (1979) and Levitt (1998) that enhancing enforcement efficiency and anction everity in order to increae expected punihment, thereby reducing criminal activity, i important. However, when dealing with organized crime that engage in corruption to manipulate conviction probabilitie, complementary meaure, uch a crack down on corruption or the intitutionalization of check and balance, are warranted to control the problem. 8 Our model deliver tark concluion with repect to the relationhip between crime and corruption and a to why the tandard crime and punihment framework may fail for ome countrie. When corruption i pervaive, further effort to inflict tougher entence on criminal will jut raie the rent to organized crime. More generally the enforcement of property right at large can break down once the police force and court top functioning properly. Beyond a threhold further policing and anction can be a catalyt to corruption in the jutice ytem. A crime and corruption become trategic complement, increaing return in variou type of crime may take off. Thi obervation may explain crime dynamic in ome countrie (e.g. Colombia and Ruia) or region within countrie (e.g. Sicily in Italy). Once thi proce tart, the bet policy may be to contain diffuion of corruption by organized crime to neighboring juridiction. Before it tart, the bet policy may be to try to uppre organized crime rent. In term of policy formulation, thi inight i related to the Luca (1976) critique. To evaluate the effect of a policy change, we need to incorporate in the analyi potential adjutment in the behavior of agent in repone to the new policy. The intended outcome from crime deterrence meaure may not materialize if 8 See e.g., Kugler and Roenthal (2004) for an analyi about eparation of power in Colombia on the importance of check and balance to buttre the legal ytem in an environment with weak governance. 22

24 the policy regime change lead criminal to intenify corruption. iven the complementarity between crime and corruption, and ince building the required intitution for a tranparent legal ytem can take a long time to achieve, tolerating ome degree of illegality (or of a ocially harmful activity which i legalized) can be deirable if it help to detroy the rent of organized crime. It i intereting to oberve that, in the 1920, after prohibition wa introduced in the United State, organized crime did have police, judge and politician in it payroll. In thi period of time, increaed police monitoring and invetigation of alcohol ditribution, a well a further law againt it, only increaed the rent of the buine for both trafficker and corrupt enforcer. On the one hand, in ome ene, evere anction on alcohol conumption owed the eed for very powerful cartel. On the other hand, the detruction of rent through legalization had a lating effect in weakening the influence of organized crime on the legal ytem, which had facilitated all kind of illegal ubidiary operation by the Mafia, including the intene ue violence for etablihing new turf and racketeering ring. Reference [1] Bardhan, P., Corruption and development. A review of iue. Journal of Economic Literature 35, [2] Bau, K., Battacharya, S., Mihra, A., Note on bribery and the control of corruption. Journal of Public Economic 38, [3] Becker,., Crime and punihment: An economic approach. Journal of Political Economy 76, [4] Becker., Stigler,., Law enforcement, malfeaance and the compenation of enforcer. Journal of Legal Studie 3, [5] Beley, T., MacLaren, J., Taxe and bribery: The role of wage incentive. Economic Journal 103, [6] Bowle, R., aroupa, N., Caual police corruption and the economic of crime. International Review of Law and Economic 17,

25 [7] Chang, J-J., Lai, C-C., Yang, C.C., Caual police corruption and the economic of crime: Further reult. International Review of Law and Economic 20, [8] Ehrlich, I., Participation in illegitimate activitie. Journal of Political Economy 81, [9] Fender, J., A general equilibrium model of crime and punihment. Journal of Economic Behavior and Organization 39, [10] Fiorentini,., Peltzman, S., The Economic of Organized Crime. Cambridge Univerity Pre, Cambridge. [11] aroupa, N., The economic of organized crime and optimal law enforcement. Economic Inquiry 38, [12] aroupa, N., Jellal, M Information, corruption and optimal law enforcement. CEPR Dicuion Paper Serie No [13] Kugler, M., Roenthal, H Check and balance: The aement of the intitutional eparation of political power. In: Aleina, A. (Ed.), Intitutional reform in Colombia, Chpt. 2, MIT Pre, Cambridge, Ma. [14] Kugler, M., Verdier, T., Zenou, Y Organized crime, corruption and punihment. DELTA Working Paper No , [15] Levitt, S., Juvenile crime and punihment. Journal of Political Economy 106, [16] Luca, R.E., Econometric policy evaluation: A critique. In: Brunner, K., Meltzer, A. (Ed.), The Phillip Curve and Labor Market, Vol. 1, Carnegie-Rocheter Conference on Public Policy, pp New York: North-Holland Publihing Company. [17] Malik, A.S., Avoidance, creening and optimum enforcement. Rand Journal of Economic 21, [18] Marjit, S., Shi, H., On controlling crime with corrupt official. Journal of Economic Behavior and Organization 34,